Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
n = int(input())
v = int( (math.sqrt(8 * n + 1) - 1) // 2 )
for i in range(v, 0, -1):
    z = n - i * (i + 1) / 2
    # 2z = a * (a+1)
    # a^2 + a - 2z = 0
    a = (math.sqrt(8 * z + 1) - 1) / 2
    if a == int(a) and a > 0:
        print("YES")
        exit()
print("NO")